THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

doi:10.1007/s10473-021-0520-7

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (5): 1733-1748.doi: 10.1007/s10473-021-0520-7

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THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

Yu XIAO¹, Jian XU², Engui FAN³

1. College of Information and Management Science, Henan Agricultural University, Zhengzhou 450046, China;
2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;
3. School of Mathematical Science, Fudan University, Shanghai 200433, China

Received:2019-09-11 Revised:2021-02-05 Online:2021-10-25 Published:2021-10-21
Contact: Yu XIAO E-mail:yuxiao5726@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (11901167, 11971313 and 51879045), Key scientific research projects of higher education institutions in Henan, China (18B110008).

Abstract

Abstract: In this paper, we apply Fokas unified method to study the initial boundary value (IBV) problems for nonlinear integrable equation with $3\times 3$ Lax pair on the finite interval $[0,L]$. The solution can be expressed by the solution of a $3\times 3$ Riemann-Hilbert (RH) problem. The relevant jump matrices are written in terms of matrix-value spectral functions $s(k),S(k),S_{l}(k)$, which are determined by initial data at $t=0$, boundary values at $x=0$ and boundary values at $x=L$, respectively. What's more, since the eigenvalues of $3\times 3$ coefficient matrix of $k$ spectral parameter in Lax pair are three different values, search for the path of analytic functions in RH problem becomes a very interesting thing.

Key words: integral equation, initial boundary value problems, Fokas unified method, Riemann-Hilbert problem

CLC Number:

35Q58

Yu XIAO, Jian XU, Engui FAN. THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL[J].Acta mathematica scientia,Series B, 2021, 41(5): 1733-1748.

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References

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THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

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